When President Obama signed a sweeping $15 billion bill to end delays at Department of Veterans Affairs hospitals two years ago, lawmakers standing with him applauded the legislation as a bold response that would finally break the logjam.

It has not quite worked out that way.

Although veterans say they have seen improvement under the bill, it has often fallen short of expectations. Nowhere is the shortfall more clear than in the wait for appointments: Veterans are waiting longer to see doctors than they were two years ago, and more are languishing with extreme waiting times.

According to the agency’s most recent data, 526,000 veterans are waiting more than a month for care. And about 88,000 of them are waiting more than three months.

“We’re making progress, yes,” Senator Johnny Isakson, the Georgia Republican who is the chairman of the Senate Veterans Affairs Committee, said in an interview. “Whether it is enough is another question.”

The push for legislative overhaul started with reports that dozens of veterans had died waiting for care at a hospital in Phoenix, while leaders hid delays and collected bonuses. An investigation by the White House found similar manipulations at dozens of hospitals, and it led to the resignation in May 2014 of the secretary of veterans affairs at the time, Eric Shinseki.

Recently, Donald J. Trump, the Republican presidential candidate, has seized on problems in health care for veterans, calling the waits for appointments “totally inexcusable” and saying that, if elected, he would crack down on employees who fail to serve veterans.

“We’re going to take care of our veterans like they’ve never been taken care of before,” Mr. Trump told the audience at the Veterans of Foreign Wars convention last week.

In a speech on Monday to the thousands who had gathered for the Disabled American Veterans national convention, Mr. Obama called the nation’s responsibility to veterans “a sacred covenant,” and he said his administration had made strides housing homeless veterans and reducing a backlog of benefits applications. But he acknowledged that improving health care is still a work in progress.

“Veterans who at times have struggled to get care at the V.A., you deserve better,” he said.

Cutting the Wait for Care

The Fix: The new law offered a two-pronged solution for the wait time problem: Let some veterans go to private doctors to provide immediate relief for the system, and hire thousands more doctors to meet long-term demand.

Did It Work? It’s complicated, but not so far.

The Breakdown: The department has added millions of square feet of new medical space. It also processes patients 10 percent more efficiently, according to agency data.

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President Obama and the veterans affairs secretary, Robert McDonald, on Monday after they attended the Disabled American Veterans national convention.CreditAl Drago/The New York Times

But instead of going down, the average wait time for primary care has gone up slightly since 2014, according to the data. More troubling, the number of veterans waiting longer than 30 days has increased by nearly 50 percent. And those who must wait more than three months has more than doubled.

Even so, Robert McDonald, the secretary of veterans affairs, says the longer waits are because the care at veterans hospitals is getting better.

Most veterans have other sources of health care, either a program like Medicare or private insurance, Mr. McDonald said in an interview, but they move to cheaper health care through the Department of Veterans Affairs if it is reasonably accessible. “As we have improved the care, what we have discovered across the country is more and more people want to come to the V.A.,” he said.

In some communities, the waiting problem is much worse. In July, veterans in Roseburg, Ore., waited twice as long to see a specialist than the average veteran. In Denver and Fayetteville, N.C., more than one-fifth of all patients must wait more than a month for appointments.

Watchdog groups and federal audits suggest that it is hard to accurately assess progress because the agency’s estimates are unreliable. Veterans say that staff members at the department still manipulate the books to make the next available appointment appear as the veteran’s first choice — a trick that makes waits appear minimal even if they stretch for months.

Government audits recently confirmed the practice in Houston and Albuquerque. In Colorado Springs, a recent audit found records were changed to show that veterans had same-day appointments when they actually waited an average of 76 days.

Sending Veterans to Private Doctors

The Fix: The law set aside $10 billion for private care. Any veteran waiting more than 30 days for an appointment or living more than 40 miles from a Department of Veterans Affairs clinic has the choice of going to a private doctor.

Did It Work? Yes, but it has created its own delays.

The Breakdown: Nearly 800,000 veterans have used the so-called Choice Program to make appointments with private doctors. But lawmakers and veterans groups say the program was hastily constructed.

“Long story short: It has major problems, not the least of which is the pure confusion that veterans and even V.A. employees have in working the program,” said Garry Augustine, director of Disabled American Veterans.

Veterans are required to call a private contractor to authorize and schedule appointments with private doctors, a process that veterans have said can take weeks. By the time a veteran sees a doctor, Mr. Augustine said, waits can be the same or longer than they would have been at a veterans hospital.

If a private doctor decides a patient needs an additional scan or test that was not authorized for the visit, paperwork must go back to the department; that can add several more weeks.

“The bottleneck is still back in the V.A.,” said Dr. Sam Foote, a retired physician who was one of the primary whistle-blowers in the scandal.

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Sharon Helman, the Phoenix medical system director at the center of a scandal on wait times for veterans, could get her job back.CreditVeterans Affairs Department, via Associated Press

Also, many private doctors report waiting months to get reimbursed. “We are hearing doctors say they won’t take part in the program because they aren’t getting paid,” said Representative Jeff Miller, the Florida Republican who is chairman of the House Veterans Affairs Committee. He added that the agency has $100 million in unpaid bills in his state.

The agency says it is working to streamline its scheduling and payment process, while adding more doctors to cut waits.

Hiring More Doctors

The Fix: The law gave the department $5 billion to hire the 28,000 health care providers the department estimated it needed to meet demand.

Did It Work? Yes, but not as well as hoped.

The Breakdown: The veterans health system has added about 19,000 employees — 68 percent of its goal. That includes more than 6,700 nurses and 1,551 doctors.

But, at the same time, the number of medical staff members either quitting or retiring has increased 30 percent since 2011, according to a report last week by the Government Accountability Office.

The agency says the losses are driven by improvement in the overall economy, but the report notes that 21 percent of departing employees said they left because of “dissatisfaction with certain aspects of the work, such as concerns about management and obstacles to getting the work done.”

It is unclear how many positions in the system are still unfilled. An agency spokeswoman said it cannot track vacancies for specific job categories.

Firing Employees Who Hid Wait Times

The Fix: The law made it faster to fire executives who concealed the scandal, and it limited their appeals in an effort to cut a firing process that could take years down to 28 days.

Did It Work? No.

The breakdown: At the signing of the bill, Mr. Obama said: “If you engage in an unethical practice, if you cover up a serious problem, you should be fired. Period.” But since then, just nine people have been fired for manipulating wait times, according to the agency. And some of them, including Sharon Helman, the Phoenix medical system director at the center of the scandal, could get their jobs back.

Ms. Helman was fired in 2014, but she contested her termination in federal court, arguing that the new rules limiting her right to appeal were unconstitutional. A ruling is pending. In May, however, the Justice Department announced that it would not contest Ms. Helman’s claim, and in June, the Department of Veterans Affairs said it would stop using the enhanced firing authority.

The move has angered many in Congress, who are now working on more new rules to make it easier to fire agency executives.

“If you don’t have accountability, and you know your job is safe whether you perform or not, it’s hard to make any progress,” Mr. Isakson said. “Right now, that is what we have at the V.A.”

A version of this article appears in print on , on Page A9 of the New York edition with the headline: The Results From Obama’s V.A. Reform? Still Waiting.. Order Reprints | Today’s Paper | Subscribe